The CRESST experiment seeks hypothetical WIMP particles that could account for the bulk of dark matter in the Universe. The detectors are cryogenic calorimeters in which WIMPs would scatter elastically on nuclei, releasing phonons. The first phase of the experiment has successfully deployed several 262 g sapphire devices in the Gran Sasso underground laboratories. A main source of background has been identified as microscopic mechanical fracturing of the crystals, and has been eliminated, improving the background rate by up to three orders of magnitude at low energies, leaving a rate close to one count per day per kg and per keV above 10 keV recoil energy. This background now appears to be dominated by radioactivity, and future CRESST scintillating calorimeters which simultaneously measure light and phonons will allow rejection of a great part of it.

To appear in the proceedings of the CAPP2000 Conference, Verbier, Switzerland, July, 2000 (eds J. Garcia-Bellido, R. Durrer, and M. Shaposhnikov)